Question

Iron pyrite, often called "fool's gold," has the formula \(\mathrm{FeS}_{2}\). If you could convert \(15.8 \mathrm{kg}\) of iron pyrite to iron metal, what mass of the metal would you obtain?

Short answer

You would obtain approximately 7.36 kg of iron metal.

Step-by-step solution

Write the Formula for Pyrite

The chemical formula for iron pyrite (fool's gold) is \(\text{FeS}_2\). This means that each molecule of iron pyrite contains one atom of iron (Fe) and two atoms of sulfur (S).

Determine the Molar Mass

Calculate the molar mass of iron pyrite (\(\text{FeS}_2\)). - Atomic mass of Fe \(= 55.85\, \text{g/mol}\)- Atomic mass of S \(= 32.07\, \text{g/mol}\) So, molar mass of \(\text{FeS}_2 = 55.85 + 2 \times 32.07 = 119.99\, \text{g/mol}\).

Calculate Moles of Iron Pyrite

Convert 15.8 kg of iron pyrite to grams: \(15.8\, \text{kg} = 15800\, \text{g}\). Using the molar mass, calculate the moles of iron pyrite:\[\text{Moles of FeS}_2 = \frac{15800\, \text{g}}{119.99\, \text{g/mol}}\approx 131.7\, \text{mol}.\]

Determine Moles of Iron

Since one mole of \(\text{FeS}_2\) contains one mole of Fe, 131.7 moles of \(\text{FeS}_2\) will contain 131.7 moles of iron (Fe).

Calculate Mass of Iron

Now, calculate the mass of the iron using its atomic mass:\[\text{Mass of Fe} = 131.7\, \text{mol} \times 55.85\, \text{g/mol} \approx 7355.3\, \text{g}.\]

Convert Mass to Kilograms

Convert the mass of iron from grams to kilograms:\(7355.3\, \text{g} = 7.3553\, \text{kg}\).

Key concepts

Molar Mass Calculation

Understanding molar mass is crucial in stoichiometry, as it provides the bridge between a substance's macroscopic mass and the microscopic world of atoms and molecules.
To calculate the molar mass, we sum up the masses of all the atoms present in the molecule. These atomic masses are available on the periodic table, listed in atomic mass units (amu), or grams per mole (g/mol) for practical use.

• For instance, in iron pyrite, \( ext{FeS}_2 \), we find that iron (Fe) has an atomic mass of 55.85 g/mol.
• Each sulfur (S) atom has an atomic mass of 32.07 g/mol. Since there are two sulfur atoms in the compound, their combined mass is \(2 imes 32.07 = 64.14 ext{ g/mol}\).

Therefore, the molar mass of iron pyrite, \( ext{FeS}_2 \), is \( 55.85 + 64.14 \), resulting in \( 119.99 ext{ g/mol} \).
Using the molar mass, you can modify mass in grams to moles, which is pivotal in stoichiometric calculations.

Iron Pyrite

Iron pyrite is often referred to as "fool's gold" because of its metallic luster and pale brass-yellow hue, which strikingly resemble real gold.
Its chemical formula is \( ext{FeS}_2 \), reflecting its composition of one iron (Fe) atom bound to two sulfur (S) atoms.
Despite its appearance, pyrite is a sulfide mineral and holds no significant monetary value apart from its potential use in some industries. Understanding its chemical structure and properties is essential in performing reactions, such as converting iron pyrite to pure iron.

• In geological settings, iron pyrite is found in various rock formations, including sedimentary and metamorphic strata.
• Typically, it forms at high and low temperatures, making it abundant in different environments.

Recognizing the distinct chemical makeup of iron pyrite is key to extracting its components through chemical reactions.

Chemical Reactions

Chemical reactions play a pivotal role in converting one substance into another.
In the context of the given exercise, the chemical reaction involves converting iron pyrite to iron metal.
Though not explicitly detailed in the problem, the conversion likely involves roasting, where iron pyrite is heated in the presence of oxygen to produce iron oxide \( ext{(FeO, Fe}_2 ext{O}_3) \) and sulfur dioxide \(( ext{SO}_2)\).

• This is followed by further steps to reduce the oxides to elemental iron (Fe), often involving reductive agents like carbon monoxide or coke.
• The general steps may not always occur in simple conditions, thus making practical applications crucial for a real-world context.

Understanding chemical reactions is vital for such mass conversions, emphasizing a balance in atoms and mass to accurately predict outcomes.

Mass Conversion

Mass conversion is an essential concept in stoichiometry, ensuring that calculations translate correctly between units during chemical processing.
In the problem, converting the mass from kilograms to grams is a necessary step, as chemical equations involve mass in grams.
The initial mass of iron pyrite, 15.8 kg, must first be changed to 15800 g to allow for further calculations. This step allows for easier subsequent calculations involving moles and molar mass.

• Understanding the relation of units and ensuring proper conversion can prevent significant errors in practical applications.
• After obtaining the desired mass in grams, converting back to kilograms may be beneficial for a final presentation of results, particularly when reporting significant values.

Ensuring a clear grasp on mass conversion between units directly influences the accuracy of stoichiometric results.